
When \(\lambda _{n,j}=0\)  for \(j=1,\dots ,p_n\) , the method reduces to the maximum composite likelihood estimator and when \(\lambda _{n,j}=\lambda _n\)  to the standard lasso estimator. If \(\beta _1\)  acts as an intercept, meaning that \(z_1(u)=1, \forall u \in D_n\) , it is often desired to let this parameter free. This can be done by setting \(\lambda _{n,1}=0\)  in the second term of (REF ). The choice of \(\mu _n\)  as a normalization factor in (REF )
follows the implementation of the adaptive lasso procedure for generalized linear models in the standard software (e.g. R package glmnet [1]}).
